Use this triangle circumradius calculator to calculate triangle circumcircle radius from its sides. Learn the triangle circumradius formula in practice.
R = circumradius of triangle
a, b, c = sides of triangle
s = semiperimeter = (a + b + c)/2
The triangle circumradius formula calculates the radius of the circumscribed circle around a triangle.
| a | b | c | Circumradius R |
|---|---|---|---|
| 3 | 4 | 5 | 2.500000 |
| 5 | 5 | 6 | 3.535534 |
| 6 | 8 | 10 | 5.000000 |
| 7 | 10 | 12 | 6.636387 |
| 8 | 15 | 17 | 9.485281 |
To manually calculate triangle circumcircle radius:
1. Compute semiperimeter s = (a + b + c)/2.
2. Compute R = (a × b × c) / (4 × √(s(s−a)(s−b)(s−c))).
3. The result is the circumradius of the triangle.
This triangle circumradius calculator instantly computes the circumradius using the triangle circumradius formula with six-decimal precision.
• The circumcenter is the intersection of perpendicular bisectors.
• All triangles have a unique circumcircle.
• The circumradius is useful in trigonometry and geometry.
• For right triangles, the circumradius is half the hypotenuse.
• Circumradius appears in engineering and navigation problems.